Mastering the Order of Operations | Solving Equations Step-by-Step

3 (5x – 2) + 2 = 26

To solve the equation 3(5x – 2) + 2 = 26, we will follow a step-by-step process called the order of operations

To solve the equation 3(5x – 2) + 2 = 26, we will follow a step-by-step process called the order of operations. This process ensures that we solve the equation correctly.

Step 1: Distribute
We will start by distributing the 3 to the terms inside the parentheses:
3 * 5x – 3 * 2 + 2 = 26
15x – 6 + 2 = 26

Step 2: Combine like terms
Next, we combine the constants -6 and 2:
15x – 4 = 26

Step 3: Isolate the variable
To isolate the variable, we need to get rid of the constant term -4. We can do this by adding 4 to both sides of the equation:
15x – 4 + 4 = 26 + 4
15x = 30

Step 4: Solve for x
To solve for x, we divide both sides of the equation by the coefficient of x, which is 15:
15x / 15 = 30 / 15
x = 2

Therefore, the solution to the equation 3(5x – 2) + 2 = 26 is x = 2.

Definition: Order of Operations
The order of operations is a set of rules that dictate the sequence in which different mathematical operations should be performed in an expression or equation to ensure the correct result. The order of operations is often summarized using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Following these rules ensures that mathematical expressions or equations are solved correctly and consistently.

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